Here's how you should not do it (I think):
If C is zero you can immediately see you have the equation of a parabola with a vertical axis of symmetry. (This eliminates two answers)
Suppose c) is the answer. It's obvious you don't have a parabola.
So one answer remains.

BTW: A parab. with a vertical axis of symmetry has the form y=a(x-b)^2+c